Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911

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Discussion Overview

The discussion centers on finding all integer solutions for the equation \((A+3B)(5B+7C)(9C+11A)=1357911\). The scope includes mathematical reasoning and problem-solving related to integer equations.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests starting by finding the prime factors of 1357911, noting that there are five factors, and then forming all groups of three factors.

Areas of Agreement / Disagreement

The discussion is in its early stages, and no consensus has been reached. There are no competing views presented yet.

Contextual Notes

Limitations include the need for further exploration of the prime factorization and the implications for forming groups of factors, which may depend on additional assumptions about the variables.

Who May Find This Useful

Participants interested in integer equations, factorization techniques, and mathematical problem-solving may find this discussion relevant.

anemone
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Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.
 
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I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.
 
Hi HallsofIvy!

Thanks for your reply. But since this is a challenge question, I hope you know our expectation here is to receive a full solution, no more, no less. (Happy)
 
No solution because

RHS is odd so all factors are odd so each term in the LHS is odd. there are 3 terms on the LHS and so their sum has to be odd.

but sum is 12A + 8B + 16C which is even so impossible
 

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